Description of fast matrix multiplication algorithm: ⟨2×26×28:1106⟩

Algorithm type

XY24Z+2XY23Z+2XY22Z+3XY21Z+2XY20Z+3XY19Z+2XY18Z+3XY17Z+4XY16Z+5XY15Z+8XY14Z+4XY13Z+7XY12Z+6XY11Z+6XY10Z+5XY9Z+3XY8Z+2X2Y5Z2+4XY7Z+26X2Y4Z2+3XY6Z+136X2Y3Z2+2XY5Z+186X2Y2Z2+4XY4Z+26XY3Z+149XY2Z+502XYZXY24Z2XY23Z2XY22Z3XY21Z2XY20Z3XY19Z2XY18Z3XY17Z4XY16Z5XY15Z8XY14Z4XY13Z7XY12Z6XY11Z6XY10Z5XY9Z3XY8Z2X2Y5Z24XY7Z26X2Y4Z23XY6Z136X2Y3Z22XY5Z186X2Y2Z24XY4Z26XY3Z149XY2Z502XYZX*Y^24*Z+2*X*Y^23*Z+2*X*Y^22*Z+3*X*Y^21*Z+2*X*Y^20*Z+3*X*Y^19*Z+2*X*Y^18*Z+3*X*Y^17*Z+4*X*Y^16*Z+5*X*Y^15*Z+8*X*Y^14*Z+4*X*Y^13*Z+7*X*Y^12*Z+6*X*Y^11*Z+6*X*Y^10*Z+5*X*Y^9*Z+3*X*Y^8*Z+2*X^2*Y^5*Z^2+4*X*Y^7*Z+26*X^2*Y^4*Z^2+3*X*Y^6*Z+136*X^2*Y^3*Z^2+2*X*Y^5*Z+186*X^2*Y^2*Z^2+4*X*Y^4*Z+26*X*Y^3*Z+149*X*Y^2*Z+502*X*Y*Z

Algorithm definition

The algorithm ⟨2×26×28:1106⟩ is taken from:

John Edward Hopcroft and Leslie R. Kerr. On minimizing the number of multiplication necessary for matrix multiplication. SIAM Journal on Applied Mathematics, 20(1), January 1971. [DOI]

Algorithm description

These encodings are given in compressed text format using the maple computer algebra system. In each cases, the last line could be understood as a description of the encoding with respect to classical matrix multiplication algorithm. As these outputs are structured, one can construct easily a parser to its favorite format using the maple documentation without this software.


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